The cut loci and the conjugate loci on ellipsoids

Jin Ichi Itoh, Kazuyoshi Kiyohara

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

We prove that the cut locus of any point on any ellipsoid is an arc on the curvature line through the antipodal point. Also, we prove that the conjugate locus has exactly four cusps, which is known as the last geometric statement of Jacobi.

Original languageEnglish
Pages (from-to)247-264
Number of pages18
JournalManuscripta Mathematica
Volume114
Issue number2
Publication statusPublished - Jun 2004

Fingerprint

Cut Locus
Ellipsoid
Locus
Cusp
Jacobi
Arc of a curve
Curvature
Line

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The cut loci and the conjugate loci on ellipsoids. / Itoh, Jin Ichi; Kiyohara, Kazuyoshi.

In: Manuscripta Mathematica, Vol. 114, No. 2, 06.2004, p. 247-264.

Research output: Contribution to journalArticle

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